Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Difference of Two Squares
problem
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Difference of two squares

Age
14 to 16
Challenge level
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What is special about the difference between squares of numbers adjacent to multiples of three?
Impossibilities
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Impossibilities

Age
11 to 14
Challenge level
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Just because a problem is impossible doesn't mean it's difficult...

Cryptarithms
problem
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Cryptarithms

Age
11 to 14
Challenge level
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Can you crack these cryptarithms?
Overlaps
problem
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Overlaps

Age
11 to 14
Challenge level
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Can you find ways to put numbers in the overlaps so the rings have equal totals?
School fair necklaces
problem
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School fair necklaces

Age
5 to 11
Challenge level
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How many possible symmetrical necklaces can you find? How do you know you've found them all?
Compare the Cups
problem
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Compare the cups

Age
5 to 7
Challenge level
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You'll need a collection of cups for this activity.

Count the Crayons
problem
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Count the crayons

Age
5 to 7
Challenge level
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How could you estimate the number of pencils/pens in these pictures?
Difference Sudoku
problem
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Difference sudoku

Age
14 to 16
Challenge level
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Use the differences to find the solution to this Sudoku.
Doubling Fives
problem
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Doubling fives

Age
5 to 7
Challenge level
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This activity focuses on doubling multiples of five.

Play to 37
problem
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Play to 37

Age
7 to 11
Challenge level
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In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.